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Maass
Hilbert
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Elliptic curves over
Q
\Q
Q
Elliptic curves over
Q
(
α
)
\Q(\alpha)
Q
(
α
)
Genus 2 curves over
Q
\Q
Q
Higher genus families
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F
q
\F_{q}
F
q
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p
p
p
-adic fields
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Weight
Degree
Include irrational
S
T
0
\mathrm{ST}^0
S
T
0
Maximal
no
yes
SO(1)
SO(2)
SO(3)
SO(4)
SO(5)
SO(6)
U(1)
SU(2)
U(1)_2
SU(2)_2
U(1)xU(1)
U(1)xSU(2)
SU(2)xSU(2)
USp(4)
U(1)_3
SU(2)_3
U(1)xU(1)_2
SU(2)xU(1)_2
U(1)xSU(2)_2
SU(2)xSU(2)_2
U(1)^3
U(1)^2xSU(2)
U(1)xSU(2)^2
SU(2)^3
U(1)xUSp(4)
SU(2)xUSp(4)
U(3)
USp(6)
yes
no
Components
Component group
P
r
[
a
1
=
0
]
\mathrm{Pr}[a_1=0]
P
r
[
a
1
=
0
]
Second trace moment
Fourth trace moment
First
a
2
a_2
a
2
moment
Sort order
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degree
real dimension
component group
trace zero density
character diagonal
columns to display
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✓ weight
✓ degree
✓ real dimension
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✓ name
✓ components
✓ Pr[t=0]
✓ E[a_1^2]
✓ E[a_1^4]
E[a_1^6]
E[a_1^8]
E[a_1^{10}]
E[a_1^{12}]
✓ E[a_2]
E[a_2^2]
E[a_2^3]
E[a_2^4]
E[a_2^5]
E[a_2^6]
E[a_3^2]
E[a_3^4]
E[a_3^6]
maximal
rational
diagonal
show all
Results (unique match)
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Label
Wt
Deg
d
i
m
R
\mathrm{dim}_{\mathbb{R}}
d
i
m
R
G
0
\mathrm{G}^0
G
0
Name
G
/
G
0
\mathrm{G}/\mathrm{G}^0
G
/
G
0
P
r
[
t
=
0
]
\mathrm{Pr}[t\!=\!0]
P
r
[
t
=
0
]
E
[
a
1
2
]
\mathrm{E}[a_1^2]
E
[
a
1
2
]
E
[
a
1
4
]
\mathrm{E}[a_1^4]
E
[
a
1
4
]
E
[
a
1
6
]
\mathrm{E}[a_1^6]
E
[
a
1
6
]
E
[
a
1
8
]
\mathrm{E}[a_1^8]
E
[
a
1
8
]
E
[
a
1
10
]
\mathrm{E}[a_1^{10}]
E
[
a
1
1
0
]
E
[
a
1
12
]
\mathrm{E}[a_1^{12}]
E
[
a
1
1
2
]
E
[
a
2
]
\mathrm{E}[a_2]
E
[
a
2
]
E
[
a
2
2
]
\mathrm{E}[a_2^2]
E
[
a
2
2
]
E
[
a
2
3
]
\mathrm{E}[a_2^3]
E
[
a
2
3
]
E
[
a
2
4
]
\mathrm{E}[a_2^4]
E
[
a
2
4
]
E
[
a
2
5
]
\mathrm{E}[a_2^5]
E
[
a
2
5
]
E
[
a
2
6
]
\mathrm{E}[a_2^6]
E
[
a
2
6
]
E
[
a
3
2
]
\mathrm{E}[a_3^2]
E
[
a
3
2
]
E
[
a
3
4
]
\mathrm{E}[a_3^4]
E
[
a
3
4
]
E
[
a
3
6
]
\mathrm{E}[a_3^6]
E
[
a
3
6
]
Maximal
Rational
Diagonal
1.6.N.216.92a
1
1
1
6
6
6
1
1
1
U
(
1
)
3
\mathrm{U}(1)_{3}
U
(
1
)
3
D
(
6
,
6
)
D(6,6)
D
(
6
,
6
)
216
216
2
1
6
37
/
108
37/108
3
7
/
1
0
8
2
2
2
18
18
1
8
320
320
3
2
0
7490
7490
7
4
9
0
195552
195552
1
9
5
5
5
2
195552
195552
1
9
5
5
5
2
1
1
1
5
5
5
34
34
3
4
317
317
3
1
7
3396
3396
3
3
9
6
39093
39093
3
9
0
9
3
8
8
8
840
840
8
4
0
185080
185080
1
8
5
0
8
0
✓
[
1
,
2
,
4
,
6
,
7
,
26
,
32
,
40
,
62
,
38
,
20
,
125
,
164
,
320
,
602
,
308
,
295
,
704
,
562
,
204
]
[1, 2, 4, 6, 7, 26, 32, 40, 62, 38, 20, 125, 164, 320, 602, 308, 295, 704, 562, 204]
[
1
,
2
,
4
,
6
,
7
,
2
6
,
3
2
,
4
0
,
6
2
,
3
8
,
2
0
,
1
2
5
,
1
6
4
,
3
2
0
,
6
0
2
,
3
0
8
,
2
9
5
,
7
0
4
,
5
6
2
,
2
0
4
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV